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‘Lock her up!’ delegates chant during prosecution of Clinton on Trump’s big day.

Celebrity mogul Donald Trump has achieved a landmark moment in American political history, completing his unlikely conquest of the Republican Party.

But Republicans who gathered for their national convention in Cleveland celebrated Trump's triumphant milestone of officially becoming the party's nominee for president not by promoting his personal virtues and policy ideas so much as by leading a three-hour prosecution of Democrat Hillary Clinton.

There were allegations that she had enabled sexual abuse at the hands of her husband. She was accused of having sympathy for Lucifer. There were so many references to her private email server and the 2012 Benghazi attacks that it was hard to keep count.

New Jersey Governor Chris Christie led a call-and-response prosecution of her actions as Secretary of State, turning the audience into an ad hoc jury: "Guilty or not guilty?" The crowd interrupted him four times: "Lock her up!" the delegates chanted. "Lock her up!"

The convention's first two nights have been striking for the unusual amount of time spent demonising Clinton, the expected Democratic nominee, as opposed to rounding out the image of the party's polarising standard-bearer.

The programme was choreographed to promote party unity under the banner, "Make America Work Again," but there were sparse references to economic policies or job growth. Instead, convention viewers were served a buffet of scattered messages and discordant themes, underscoring the party's divisions and discomfort with Trump. For instance, overhauling trade deals has been a cornerstone of Trump's economic agenda, yet there was relatively little mention of his ideas about trade. Nor were there many mentions of his other signature ideas: building a wall on the southern US border, temporarily barring foreign-born Muslims from entering the country and deporting undocumented immigrants en masse.

House Speaker Paul Ryan gave the most substantive and muscular speech about conservatism. But the man who four years ago got a rock-star reception at the GOP convention as Mitt Romney's vice-presidential running mate was coolly received by Trump delegates in the convention hall. Ryan, who has uneasily endorsed Trump, spoke mostly about his own agenda for House Republicans. Addressing the turmoil Trump has wrought on the party, Ryan said, "Democracy is a series of choices. We Republicans have made our choice". He added: "Have we had our arguments this year? Sure we have. You know what I call those? Signs of life - signs of a party that's not just going through the motions, not just mouthing new words for the same old stuff".

The most effective character testimonials came from two members of the Trump family - Donald jnr and Tiffany - who tried to convince people their father is more compassionate and trustworthy than the caricature of Trump.

"Donald Trump has never done anything halfway, least of all as a parent," said Tiffany, 22, his daughter from his second marriage with Marla Maples, who was in attendance. Tiffany added, "My dad is a natural-born encourager, the last person who will ever tell you to lower your sights."

Donald jnr, 38, delivered a particularly forceful defence of his father and tried to explain his appeal to blue-collar America. He described how his father mentored him at construction job sites, and he condemned a system that benefits "our new aristocrats". He said: "He didn't hide out behind a desk in an executive suite. He spent his career with regular Americans. He hung out with the guys at construction sites ... pouring concrete and hanging sheetrock."

Other speakers sought to convince voters that Trump developed unrivalled business acumen, a strategic mind and drive during his decades as a real estate baron and promoter. His career - a quest for riches and fame that was marked also by successive bankruptcies and other failings - has been the subject of an assault from Clinton and her allies.

The speakers tried to refocus the convention after a problematic opening night punctuated by Melania Trump's speech, which was well received but came under scrutiny because it contained passages nearly identical to portions of Michelle Obama's speech at the 2008 Democratic National Convention.

Trump's achievement was remarkable, if fully anticipated. A reality-television star and business mogul who entered a race against more than a dozen of the GOP's brightest stars, Trump muscled each of them out of his way. In the end, all the party had left was Trump. And it finally became his.

Trump beamed in live from Trump Tower in New York. He said: "This is a movement, but we have to go all the way. . . . We'll win the presidency and bring real change and leadership back to Washington."